Abstract.
We prove the existence of nontrivial solutions to the system
on a bounded set of \({\mathbb{R}}^N\), with nonlinear coupling at the boundary given by
The proofs are done under suitable assumptions on the potential F, and based on variational arguments. Our results include subcritical, resonant and critical growth on F.
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Supported by Univ. de Buenos Aires grant TX48, by ANPCyT PICT No. 03-00137 and by Fundación Antorchas. JFB is also supported by ANPCyT PICT No. 03-10608. JFB and JDR are members of CONICET.
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Bonder, J.F., Martínez, S. & Rossi, J.D. Existence results for Gradient elliptic systems with nonlinear boundary conditions. Nonlinear differ. equ. appl. 14, 153–179 (2007). https://doi.org/10.1007/s00030-007-5015-2
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DOI: https://doi.org/10.1007/s00030-007-5015-2